1. Field of the Invention
The present invention relates to a method for modelling the effects of the vibrations induced by a vortex on or in an elastic structure subjected to a fluid in motion.
2. Description of the Prior Art
The presence of an elastic structure in a fluid in motion and having a variable velocity in time and in space can produce instability in this fluid. The fluid creates vortices as it comes off the structure. The swirling alternating separation thus created can lead to vibrations of the structure referred to in shortened form as VIV (vortex-induced vibrations) in the description hereafter. These VIV can have a great effect, notably on the fatigue strength of the structure.
The fatigue strength or resistance of a riser or of a pipe providing effluent transfer is a major problem for oilfield development. In particular, in the case of great water depths, these pipes are subjected to stresses and vibrations that can reduce the life thereof and cause damage that can lead to breakage. Anticipating the behavior of these risers with time notably allows reduction of the maintenance costs and avoiding risks of pollution due to a possible breakage.
The term excitation designates in the description hereafter the propagation of the vibration along the structure, its damping and its natural modes. The thrust corresponds to the force exerted by the vortices on the elastic structure. The drag force corresponds to the force exerted by the current on the structure.
It is well-known to determine the response of an elastic structure subjected to external disturbances.
One of the methods implemented is described by Vandiver and Li in the instruction manual (1995) of the software marketed under the name SHEAR7. This software uses values of natural modes of the structure calculated by means of the software itself or by means of another computing software. The software then defines the thrust forces and the hydrodynamic damping for each mode, in order to obtain the amplitude response of the vibrations, as well as the life of the riser. The method is a modal approach that only takes into account the frequency variation of the vibrations, the current or external excitation being considered to be a constant in time. The variation of the disturbance is monotonic in space. The author uses a corrective coefficient to account for the correlation between the various forces.
Another procedure disclosed by Nedergaard consists in getting close to the xe2x80x9clock-inxe2x80x9d mode where the resonant frequency of the structure is close to the Strouhal frequency known to those skilled in the art. The authors account for the variation of the disturbance with space and time in order to obtain the response of the structure. However, they do not consider the influence of the various forces acting on the various natural modes of the structure.
Although taking account of the interactions between the various parameters and the various forces involved in the vibrational phenomena induced in a structure is complex, the method according to the invention allows evaluation of the response of an elastic structure subjected to a fluid in motion by taking into account the interactions of the various forces on all the natural modes of vibration.
An elastic structure is understood to be a structure wherein the vibrations can be propagated over all of its length or at least the most part of this length.
The invention is particularly well-suited for dimensioning or adaptation of a structure having a one-dimensional type dominant length.
The invention relates to a method for dimensioning or adapting an elastic structure immersed in a fluid in motion, the structure having a length Lt.
The method comprises:
a) defining the natural excitation modes of said structure and their number N are defined,
b) for at least a given time for an excitation mode of the structure, the various holding zones LR over length Lt and, for each holding zone, the excitation force FR corresponding to the excited natural mode r are determined,
c) step b) is carried out for all the natural modes defined in step a),
d) the vibration amplitude response A of the elastic structure over the greatest part of its length Lt is determined by taking into account the effect of the various excitation forces FR on each natural vibration mode defined in step a) so as to obtain a characteristic allowing dimensioning or adapting the structure to the mechanical stresses applied by the fluid in motion.
According to an embodiment, steps a) to d) are repeated for a given time interval tmax.
According to another embodiment, the value of vibration amplitude Ai for an excitation mode i and a time (txe2x88x92dt) is for example compared with the vibration amplitude values |Ai(t)| and |Ai(txe2x88x922dt)| respectively obtained at times (t) and (txe2x88x922dt), and when value |Ai(txe2x88x92dt)| is greater than these two values, it is used in steps a) to d).
According to an embodiment, the vibration amplitude is determined for a point z of the structure by splitting it up, for example, on the basis of the natural excitation modes i as follows:       A    ⁢          (      z      )        =            ∑              i        =        1            N        ⁢          xe2x80x83        ⁢                  A        i            ⁢                        Y          i                ⁢                  (          z          )                    
Ai modal amplitude being split up for a given time t on the basis of all of the excitation forces according to the relation:       A    i    =            ∑              r        ⁢                  xe2x80x83                =        1            N        ⁢          xe2x80x83        ⁢                  A        ir            ⁢      exp      ⁢              xe2x80x83            ⁢              (                  j          ⁢                      xe2x80x83                    ⁢                      ω            r                    ⁢          t                )            
with Air the vibration amplitude for a mode i and a force corresponding to subscript r.
According to an embodiment for calculating the vibration amplitude for a mode i and a force r, the history xcex93(t) of the force at the time t is used, the history being obtained by linear combination of the history of the force at the time (txe2x88x92dt) multiplied by a coefficient and the history of the force obtained on the increment dt.
According to an embodiment, the vibration amplitude Air can be calculated by splitting up the pulsation on the mode i and the force corresponding to the subscript r being considered.
The drag coefficient of the structure is for example determined.
According to another variant, at least one maximum stress value corresponding to a point z of the structure is for example determined at a given time tmax.
The fatigue value of the structure can also be determined.
The method according to the invention is for example applied for dimensioning or adapting a pipe used in oil production to the mechanical stresses applied by the wave motion or the sea currents.
According to an implementation variant of the method, the drag coefficient of the pipe and/or the stresses induced in the pipe and/or the fatigue of the pipe are determined for a pipe used in the sphere of oil production.